I know that when some kind person reveals the answer to this question I'm going to stunned that I couldn't see it without asking but here goes anyway..

Reading Keftopics about r105 crossovers it says that with fourth order crossovers each drive unit is 6dB down at the crossover frequency and that because they are in phase they add up to a total output of 0dB.

Now I understand quite happily that the drivers are in phase and that therefore they will each require less output at the crossover than they would if they were out of phase. But its the figure of 6dB I can't resolve.

Half power is 3dB or the square root of 2 in terms of volts (0.707), I get that . So why is it that I think 2 times -6dB giving 0dB is getting more power out than is going in?

I know I'm wrong but I can't see where. I would have thought that 4th order in phase crossovers would have the drivers 3dB down as two halves = a whole and other crossover slopes where they are not in phase would need higher outputs at the crossover frequency.

Please tell me where I'm a bit wonky on this. Should I book myself in somewhere?

s.p.l. is proportional to the acceleration of the diaphragm. Acceleration is proportional to the force applied to the diaphragm( F=ma). The force is proportional to the current through the voice coil (=Bli). The current is proportional to the voltage applied to the driver (I=V/R) over its usable band. The ankle bone's connected to the foot bone, now hear the word of the Lord.......

Voltage dBs are 20log base 10 of the ratio. Hence 6dB and not 3dB.
BTW, what might be confusing you is that 1st and 3rd order Butterworth filters add up at the -3dB point. But this only because they are in quadrature (at 90 deg) and not "in phase" at crossover.

Assuming that each speaker was of equal sensitivity and impedance matched to extract the full rated power of the amplifier (which they probably won't be)....
....I think it goes something like this;

one 25W amplifier into one speaker will produce 6dB less s.p.l. than one 100W amplifier into the same speaker (10log[25/100]). If you then add a second identical 25W combo there will be a 6dB increase in s.p.l . So the answer is they are equally loud (on axis in the far field). You are not getting something for nothing because you have doubled the speakers as well as the amplifier. If you put 50W into only one speaker the s.p.l would only increase by 3dB.

example; vox AC30 is 6dB louder than the AC15 - twice the power AND twice the speakers.

one 25W amplifier into one speaker will produce 6dB less s.p.l. than one 100W amplifier into the same speaker (10log[25/100]). If you then add a second identical 25W combo there will be a 6dB increase in s.p.l . So the answer is they are equally loud (on axis in the far field). You are not getting something for nothing because you have doubled the speakers as well as the amplifier. If you put 50W into only one speaker the s.p.l would only increase by 3dB.

I have banged this around in my head for hours trying to grasp what you're telling me and I'm struggling. I appreciate that there are two speakers in the example above but why the odd paradox with regard to energy?

25 watts into two spaekers (each) and 100 watts into 1 speaker just as loud? So where is the extra 50 watts of energy being lost in the single speaker system? Clearly, there is something fundamental I've not grasped here.

So where is the extra 50 watts of energy being lost in the single speaker system? Clearly, there is something fundamental I've not grasped here.

Even if the component speakers are identical, the single speaker system does not have the same transducer transfer characteristic of the double speaker system. Why should it? Read my first reply again and then think about current in the voice coils producing a force which accelerates the diaphragm mass, which in turn produces s.p.l.

The two speaker system has twice the magnetic motor with which to convert current into s.p.l. That's why half the power will still produce the same s.p.l.